Active magnetic bearings are used to suspend shafts of rotating equipment subject to load spectra which vary with respect to time. Control of the position of the rotating assemblies of such equipment is effected by electromechanical systems which combine the use of feedback control and switching amplifiers. For the practical application of such systems in industrial rotating machinery, the output of these amplifiers must vary in the order of thousands of cycles per second in order to maintain or adjust the desired position. Furthermore, the application demands that only switching amplifiers be used for reasons of efficiency.
The following discussion describes amplifiers used in magnetic bearing applications and the schemes used to control them in this application.
Switching amplifiers are almost exclusively used for magnetic bearing applications over analog amplifiers because of their much higher efficiency. Switching amplifiers have efficiencies which typically are above 90%, while analog amplifiers have efficiencies which are typically below 20%. This makes analog amplifiers impractical except for magnetic bearings with very low power requirements.
As shown in FIG. 1, a bi-directional switching amplifier 10 normally consists of an H-bridge arrangement of power switches. The H-bridge comprises two switching legs 12 and 14 with a load 16, such as a bearing coil, connected between the two switch legs 12 and 14. Leg 12 is provided with switches 18 and 20. Leg 14 is provided with switches 22 and 24. Legs 12 and 14 are connected in parallel with a power supply 26 and a capacitor 28. Each power switch is typically in the form of a field effect transistor (FET) and is responsive to a control signal 30. Two schemes are used to control the switches to allow the current to track the setpoint: bi-state switching and tri-state switching.
Bi-state switching, also known as Phase Anti-Phase Switching, uses a single control bit to control the amplifier switches. This is illustrated in FIGS. 2a and 2b. The switches operate in pairs. In State 1 (FIG. 2a), switches 18 and 24 (Amplifier pair A) are closed when the current in the amplifier 10 is increasing, while switches 20 and 22 (Amplifier pair B) are open. Conversely, in State 2 (FIG. 2b), switches 20 and 22 are closed and switches 18 and 24 are opened, and the current is decreasing. The energy is switched back and forth between the bearing coil 16 inductance and the large electrolytic capacitor 28 which lies across the power supply 26. Resistance losses from this arrangement are replenished from the power supply 26.
When the amplifier 10 is controlling a steady state current, the duty cycle of the control bit is close to 50%. The duty cycle rises to increase the current level and falls to decrease the current level. As mentioned, bi-state switching is controlled by one control bit.
The disadvantage of this scheme is the high level of switching losses and alternating current imposed on capacitor 28. These losses are incurred when switching a field effect transistor (FET) ON or OFF. When a FET is fully ON, it has very low resistance losses because of the low voltage drop across the device, and when the FET is OFF, the resistance losses are also low because the current is negligible. However, when a FET is in the process of turning ON or OFF, it has both current and voltage across it, and, as a result, it generates and dissipates heat. The amount lost during a switching action is determined by how fast the FET can be switched. The switching speed is limited by voltage spikes that can become large enough to destroy the device. Bi-state switching of the amplifier 10 requires four switching actions of the FETs per cycle.
Switching amplifiers must have large electrolytic capacitors across the supply in order to reduce the voltage variation. The bi-state switching places a square wave across the capacitor with a peak current equal to twice the load current. This current requires that very large capacitance be used in order to reduce the internal resistance of the capacitor, and thus limit the heating of the capacitor. The heating of the electrolytic capacitor reduces its life span.
The most common method of switching a bi-state amplifier 10 with a single control bit is pulse-width modulation (PWM) control. A triangle PWM wave is compared to an error signal for the amplifier 10. The error signal is a setpoint minus a current feedback signal. When the PWM wave is above the error signal, Amplifier pair A (switches 18 and 24) is active. When the PWM wave is below the error signal, Amplifier pair B (switches 20 and 22) is active.
The phase width of the amplifier is controlled by the gain in the circuit. The higher the gain, then the larger the bandwidth, and the wider range of control is available to the magnetic bearing system, which is desirable. The maximum gain is limited by the slope of the PWM triangle. The error triangle that results must not have a steeper slope than the PWM signal, or the amplifier will start switching in an unstable fashion and the amplifier will destroy itself. The slope of the error triangle is determined by the amplifier feedback gain and ratio of voltage to inductance (V/L). The amplifier gain must be changed whenever the supply voltage or the bearing coil 16 inductance is changed. This results in amplifiers with a unique gain setting for each size of magnetic bearing actuator. This increases the costs of the amplifiers, which is undesirable. The triangle PWM wave is double the slope compared to a saw tooth PWM wave and allows the current to switch around the setpoint. The slope of the PWM wave can also be increased by increasing the switching frequency, but the switching losses in the amplifier 10 also increase.
The second method used to control bi-state magnetic bearings is called Current Mode Switching. Amplifier pair A is turned ON periodically by a clock and remains ON until the current reaches the setpoint. Amplifier pair B then remains ON until the next clock. This method has a higher bandwidth, but there is always an error between the setpoint and the current which is equal to half the ripple current. The bandwidth of the amplifier is not highly dependent on the V/L ratio which allows a single design of amplifier to serve a wide range of magnetic bearing actuator sizes.
Tri-state switching uses two bits to control the FETs: a PWM bit and a Direction bit. The Direction control bit determines whether the current is decreasing or increasing. The PWM bit determines whether the bearing is connected to the power supply or is simply circulating current around the inductive load. The three states for a switching amplifier are shown in FIGS. 3a, 3b and 3c.
FIGS. 3a, 3b and 3c depict current paths within the amplifier during Discharge, Idle, and Charge states, respectively. The current-voltage relationship of the inductive load is defined by the differential equation v=-L(di/dt), where i is the current flowing through the load. Thus, the current through the load increases or decreases exponentially if a fixed voltage is applied across the load and tends to remain constant if the ends of the load are shorted together. In the Discharge state, shown in FIG. 3a, switches 18 and 24 are closed, thereby applying a voltage across the load. Therefore, the current flow decreases exponentially from zero to a steady-state value. Once the desired current through the load has been attained, switch 18 is opened and switch 20 is closed so that the Idle state illustrated in FIG. 3b is entered. In this state, the ends of the load are shorted together and the current tends to remain constant except for decay due to resistive losses. Finally, when it is desired to increase the current flowing in the load, both switches 18 and 24 are opened and switches 20 and 22 are closed so that the Charge state illustrated in FIG. 3c is entered. In this state, the power supply voltage is applied across the load in a polarity opposite that of the Discharge state. Thus, the current flowing through the load increases exponentially.
The tri-state amplifier always goes into State 2, the Idle state, after being in charge or discharge State. This means the amplifier makes only two switches during a switching cycle instead of four. An amplifier running with tri-state switching, therefore, has only half the switching losses of the same amplifier run in a bi-state switching mode, an advantage which is desirable.
The second advantage to tri-state switching is that the current on the electrolytic capacitor is greatly reduced. This is because the current in the bearing is circulated in the bearing in the Idle State instead of being placed back on the capacitor. The lower current in the capacitor will reduce heating and extend the capacitor life. This increases the reliability of the system which is very desirable.
The common method controlling tri-state switching is PWM using a saw tooth reference. A saw tooth PWM wave is compared against the feedback error. At the beginning of the saw tooth, the direction bit is set depending on whether the feedback error is negative or positive. The PWM remains asserted until the feedback error is less than the PWM signal. Once again, the slope of the feedback error must not be above the slope of the PWM saw tooth reference, and the feedback gain requires different settings for different sizes of bearing actuator.